Equal volumes of water and alcohol when put in similar calorimeters take $$100$$ $$sec$$ and $$74$$ $$sec$$ respectively to cool from $$500C$$ to $$400C$$. The thermal capacity of each calorimeter is numberically equal to the volume of either liquid. The specific gravity of alcohol is $$0.8$$. If the specific heat capacity of water is $$1$$ $$cal/gm$$, the specific heat capacity of alcohol will be

Question

Equal volumes of water and alcohol when put in similar calorimeters take $$100$$ $$sec$$ and $$74$$ $$sec$$ respectively to cool from $$500C$$ to $$400C$$. The thermal capacity of each calorimeter is numberically equal to the volume of either liquid. The specific gravity of alcohol is $$0.8$$. If the specific heat capacity of water is $$1$$ $$cal/gm$$, the specific heat capacity of alcohol will be

Infinity Learn · Accepted Answer

Let V be the volume of either liquidThermal capacity of each calorimeter is V cap per  $$0CMass$$ of water $$=$$ V × $$1$$ $$=$$ V gMass of alcohol $$=$$ V × $$0.8$$ $$=$$ $$0.8$$ VgRate of colling of water,  $$=$$ $$1100$$[$$V(50-40)+V$$×$$1$$×(50-40)] $$=$$ $$V5$$ $$cal/secRate$$ of cooling of alcohol   $$=$$ $$174$$[$$V(50-40)+S$$×$$0.8V$$×$$10$$]  $$=$$ $$174$$[$$10V$$ $$+$$ $$8V$$×S ] Now    $$174$$[$$10V$$ $$+$$ $$8V$$×S] $$=$$ $$V5$$∴ s $$=$$ $$0.6$$ $$cal/g0C$$

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